Brazilian midfielder Kaka is expected to depart the Santiago Bernabeu should the Primera Division champions complete the signing of Luka Modric from Tottenham.
Sahin has also fallen down the pecking order in the Spanish capital and Merengues boss Jose Mourinho has indicated that he might be allowed to spend a season on loan elsewhere.
Galatasaray president Unal Aysa told calciomercato.com: "Kaka and Sahin are both set to leave. We definitely want the Brazilian.
"We like the Turk too but we face competition from Fenerbahce, Milan, Inter, Arsenal and Liverpool.
"We will only know his final destination when the transfer is complete."
Gala face stiff opposition to their pursuit of Kaka with Serie A club Milan already in negotiations to bring their former star player back to the San Siro.